On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients

Details On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients

2008-10-22

arxiv.org/abs/0810.4095v1

Mathematics

Spectral Theory

7 pages

Scientific paper

In the paper we consider singular spectral Sturm--Liouville problem $-(py')'+(q-\lambda r)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function $p\in L_{\infty}[0,1]$ is uniformly positive, generalized functions $q,r\in W_2^{-1}[0,1]$ are real-valued and unitary matrix $U\in\mathbb C^{2\times 2}$ is diagonal. The main goal is to prove that well-known (for smooth case) facts about number and distribution of zeros of eigenfunctions hold in general case.

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